Best Reaction Target To Determine Proton Distribution Radii of Atomic Nuclei
We found that a heavy target such as Pb is most suitable for determining the proton distribution radii of unstable nuclei through charge-changing cross-section ($\sigma_\text{cc}$) measurements. As a heavy ion probe, low-$Z$ targets are routinely used to determine nucleon distribution radii of unstable isotopes. This approach has recently been extended to study proton distribution radii from $\sigma_\text{cc}$ measurements. However, empirical scaling factors have to be introduced to apply the Glauber models. In the present work, we systematically investigated the scaling factor using 39 new $\sigma_\text{cc}$ data of 18 $p$-shell nuclei on hydrogen, carbon, silver, and lead targets at around 240 MeV/nucleon. Together with the existing data, we reveal a universal dependence of the scaling factor on both the masses of target nuclei and the separation energies of projectile nuclei. The scaling factors decrease with increasing target-nucleus mass and converge to 1 for the highest-$Z$ target, making the scaling unnecessary. We conclude that instead of a low-$Z$ target, employing a heavy target such as Pb in $\sigma_\text{cc}$ measurements is the best option to determine the proton distribution radii of unstable nuclei.